Consider two long parallel wires with the same length carrying currents of diffe

Question

Consider two long parallel wires with the same length carrying currents of different magnitudes. The magnitude of the force that one wire exerts on the other is F0.

A) If the current in both wires is halved, what happens to the magnitude of the magnetic force (in terms of F0) that each wire exerts on the other?

B) If the current in one wire is quadrupled and the current in the other wire is halved, what happens to the magnitude of the magnetic force (in terms of F0) that each wire exerts on the other?

Explanation / Answer

part1 :

formula for Resistance is R = rho L/A

where L is length, rho is resistitivty   and A is area = pi r^2

so when D= d/2   , r = r/2

then A new = A/4 and Lnew = L/2

so

Rnew = L/2   * 4/A   = 2 times of R

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rho is resisitivty = RA/L

Rho = 2 * 1/4   * 2/1

Rho new   = 4/4 = 1 rho

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